A stage-adaptive optimization framework for reconciling energy balance and flexibility balance in the energy transition

The escalating energy transition, characterized by the increasing penetration of renewable energy, poses significant challenges to maintaining both energy balance and flexibility balance in power system. Traditional scheduling approaches often construct static flexibility requirement intervals based on historical extreme values, leading to overly conservative resource reservation and economic inefficiency. Moreover, existing models typically treat energy balance and flexibility balance as separate constraints, overlooking their inherent coupling and stage-adaptive evolution across different transition stages. To address these limitations, this paper proposes a stage-adaptive optimization framework that characterizes flexibility requirements using probabilistic net load forecasts, reducing conservativeness while ensuring security. The framework coordinates multiple resources including thermal power, energy storage, hydrogen production, grid power exchange, and demand side response under a linear-programming-based adaptive enumeration strategy. Results across three transition stages show that deriving flexibility requirements from net load forecast errors yields narrower intervals. Compared with traditional method, the proposed framework reduces upward and downward flexibility reserves by 58.87%–77.40% and 12.75%–54.54%, respectively, leading to cost reductions of 3.94%–7.94%, carbon emission reductions of 26.56%–27.84%, and renewable energy penetration increases of 14.05%–23.15%. The framework adapts scheduling strategies to evolving conditions, offering a promising pathway for high renewable power systems.